The Cook Islands are difficult to find - in more ways than one. Scour a map of the world and you'll eventually find a series of specks somewhere near Tahiti. From Los Angeles, it's an ankle-swelling 10-hour haul. The in-flight screen map remains featureless for nine hours and 58 minutes, until the pilot somehow locates a 10-kilometre-long sliver of land.

It's 3am and all 10,000 Cook Islanders appear to be at Rarotonga airport in a meeting, greeting or touting capacity. Immigration officers with the physiques of rugby players check passports, excited relatives peer through railings and 'Ukulele' Jake serenades bleary-eyed travellers at the baggage carousel. Include the taxi drivers, tour guides and miscellaneous insomniacs, and you're left with the impression that 3am in the Cook Islands is like 6pm anywhere else.

Jet-lagged passengers sleepwalk through customs unsure of the time or even the day of the week. They have good reason to feel disoriented - the International Date Line lies over the horizon. New Zealand is a short flight to the west and 23 time zones ahead. Feeling like an extra in Back to the Future, you browse the following day's New Zealand Herald wondering if there is some way of using tomorrow's racing results to your advantage.

Rarotonga is the largest and most populous in a chain of 15 Cook Islands scattered over two million square kilometres of ocean - about two-thirds of India's land area. The entire landmass, however, is a miniscule 240 square kilometres or less than twice the size of Lantau Island. Some of the far-flung atolls are so remote it can be months before supply ships arrive.

The islands are named after Captain James Cook, the explorer who claimed the archipelago for the British Crown on his voyages of discovery in the 1770s. European missionaries came next, spreading both puritanical values and disease, to which the Polynesians had no natural immunity.

Declared a British protectorate in 1888, the Cook Islands were annexed to New Zealand in 1901. The Pacific 'neighbours' continue to share a free econo- mic association. Islanders are granted automatic New Zealand residency, New Zealand dollars are used and English is the official language, although Maori is also widely spoken.

Yachts and cargo freighters are the only way to reach the more inaccessible islands. One in particular has an intriguing history. The time-capsule islets of Palmerston lie 500 kilometres north of Rarotonga, beyond the radar of most tourists and rarely visited even by supply boats. The atolls were uninhabited until 1862, when William Marsters, an English farmhand, settled with his three Polynesian wives and started a dynasty. Today, each of Palmerston's 60-odd inhabitants is a Marsters and speaks the same Victorian Gloucestershire dialect their forefather used.

After strenuous inquiries at the harbour master's office and a couple of consolation cocktails at Trader Jacks bar, I accept that I could grow old trying to find a passage to Palmerston. Anyway, Rarotonga is starting to weave its spell, so it seems best to stay put.

More Cook Islanders live overseas than in their birthplace so the logical accommodation solution is to rent a house. There are plenty of vacant homes to choose from; rates are reasonable and what you lose in service you gain in independence.

I find a simple cottage in the verdant seaside village of Matavera, which offers tranquillity, a well-equipped kitchen and an orchard of papaya trees surrounded by lush hedges of bougainvillea and hibiscus. Cicadas chirrup and waves thump on the reef.

The stupendous scenery of Rarotonga is ideal for exploring by bicycle. A quiet coastal road encircles the island, bringing you back to where you started after three or four hours of leisurely pedalling. With so many sublime swimming and snorkelling opportunities, a morning cycle ride soon becomes a full-day expedition.

The capital of the Cook Islands is Avarua; a settlement stuck in a South Pacific time warp that only enhances its charm. The town is busiest on Saturday, when the market is in full swing. In between shopping for giant avocado and mango, locals swap gossip and discuss church outfits for the following morning.

I cycle out of Avarua wobbling under the weight of picnic provisions. Beyond the docks and the modest hut that serves as Parliament House, the road rarely strays more than a few metres from the water's edge. The coral reef fringing the lagoon ensures calm turquoise seas, schools of glittering tropical fish and the sensation of snorkelling in an aquarium.

Inland, a green carpet of vegetation softens the angular peaks, waterfalls beckon and rustic bungalows nestle among the coconut groves. Motorcycles and cars can be hired but why fill the frangipani-scented air with noise and fumes? Besides, race around and you'll miss the smiles and small talk.

The route continues alongside a stretch of unblemished beach with sand as white as washing powder. At Wigmore's Waterfall, hikers reward themselves with a swim after completing the cross-island trek. The challenging hike offers sweeping vistas from the highest point, Te Rua Manga (The Needle), but the trail is often slippery and frequent forks in the path can lead to unscheduled detours.

A few minutes' ride from the waterfall is Titikaveka Church. Cook Islanders are devout Christians and if you pedal past on a Sunday you'll be treated to rapturous singing from the faithful. The men don their starched Sunday best while the women opt for floral prints and wide-brimmed palm-frond hats. Visitors always receive a hearty welcome and are likely to be invited back to the minister's house for tea and cake.

By late afternoon, I finish my cycle tour at Muri Lagoon; a postcard photographer's favourite. A handful of tourists share the busiest beach in the Cook Islands. We sit and watch the sun slip behind the jagged hills; the tangerine and scarlet sky complementing our cocktails.

There aren't many locals enjoying the perfect Polynesian evening. With another late night at the airport ahead, they are probably fast asleep.